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June 2011 FDR control with adaptive procedures and FDR monotonicity
Amit Zeisel, Or Zuk, Eytan Domany
Ann. Appl. Stat. 5(2A): 943-968 (June 2011). DOI: 10.1214/10-AOAS399

Abstract

The steep rise in availability and usage of high-throughput technologies in biology brought with it a clear need for methods to control the False Discovery Rate (FDR) in multiple tests. Benjamini and Hochberg (BH) introduced in 1995 a simple procedure and proved that it provided a bound on the expected value, FDRq. Since then, many authors tried to improve the BH bound, with one approach being designing adaptive procedures, which aim at estimating the number of true null hypothesis in order to get a better FDR bound. Our two main rigorous results are the following: (i) a theorem that provides a bound on the FDR for adaptive procedures that use any estimator for the number of true hypotheses (m0), (ii) a theorem that proves a monotonicity property of general BH-like procedures, both for the case where the hypotheses are independent. We also propose two improved procedures for which we prove FDR control for the independent case, and demonstrate their advantages over several available bounds, on simulated data and on a large number of gene expression data sets. Both applications are simple and involve a similar amount of computation as the original BH procedure. We compare the performance of our proposed procedures with BH and other procedures and find that in most cases we get more power for the same level of statistical significance.

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Amit Zeisel. Or Zuk. Eytan Domany. "FDR control with adaptive procedures and FDR monotonicity." Ann. Appl. Stat. 5 (2A) 943 - 968, June 2011. https://doi.org/10.1214/10-AOAS399

Information

Published: June 2011
First available in Project Euclid: 13 July 2011

zbMATH: 1232.62106
MathSciNet: MR2840182
Digital Object Identifier: 10.1214/10-AOAS399

Keywords: False discovery rate , gene expression analysis , improved BH , Monotonicity

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.5 • No. 2A • June 2011
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